Is supplication answered during the Adhan, and is there any textual evidence from the Sunnah indicating that?

Supplication is permissible during the Adhan and after it. The Hadith narrations about supplication after the Adhan are clearer, more numerous, and more authentic. One who supplicates during the Adhan should not let it distract him from repeating the Adhan after the Muezzin, because repeating the Adhan becomes impossible once its time has passed, whereas supplication can still be performed after the Muezzin has finished.